This secret is hidden within the mission E1M3 "Death Row". When you start, break through the nearby glass and continue down the path until you find a chapel to your left. Shoot out or kick the stained glass on the left then examine the front side of the altar (not the side on the raised platform), which will make the room turn red (and the cross to lower and turn upside down). Head through the hole you just made in the stained glass to find an Octabrain. Kill it and continue down the path to find Doomguy. You'll know you've triggered the trophy when Duke makes a comment about the "Doomed Marine".
Below is a video that is not mine but rather was made by Thehunters97 showing how to find Doomguy. I did not make this video and all credit for it goes to Thehunters97.